1. Event-related fMRI (er-fMRI)
Klaas Enno Stephan
Translational Neuromodeling Unit (TNU) Institute for Biomedical Engineering, University of Zurich & ETH Zurich
Laboratory for Social & Neural Systems Research (SNS), University of Zurich
Wellcome Trust Centre for Neuroimaging, University College London
With many thanks for slides & images to:
FIL Methods group, particularly Rik Henson and Christian Ruff
Methods & models for fMRI data analysis November 2012

2. Overview of SPM p <0.05 Statistical parametric map (SPM)
Image time-series
Kernel
Design matrix
Realignment
Smoothing
General linear model
Statistical
inference
Gaussian
field theory
Normalisation
p <0.05
Template
Parameter estimates

3. Overview 1. Advantages of er-fMRI 2. BOLD impulse response
3. General Linear Model
4. Temporal basis functions
5. Timing issues
6. Design optimisation
7. Nonlinearities at short SOAs

4. Advantages of er-fMRI
Randomised trial order c.f. confounds of blocked designs

5. er-fMRI: Stimulus randomisation
Blocked designs may trigger expectations and cognitive sets …
Unpleasant (U)
Pleasant (P)
Intermixed designs can minimise this by stimulus randomisation … … … … …
Pleasant (P)
Unpleasant (U)
Unpleasant (U)
Pleasant (P)
Unpleasant (U)

6. Advantages of er-fMRI
Randomised trial order c.f. confounds of blocked designs
Post hoc classification of trials e.g. according to performance or subsequent memory

7. er-fMRI: post-hoc classification of trials
Participant response:
„was not shown as picture“
„was shown as picture“
 Items with wrong memory of picture („hat“) were associated with more occipital activity at encoding than items with correct rejection („brain“)
Gonsalves & Paller (2000) Nature Neuroscience

8. Advantages of er-fMRI
Randomised trial order c.f. confounds of blocked designs
Post hoc classification of trials e.g. according to performance or subsequent memory
Some events can only be indicated by the subject e.g. spontaneous perceptual changes

9. eFMRI: “on-line” event-definition
Bistable percepts
Binocular rivalry

10. Advantages of er-fMRI
Randomised trial order c.f. confounds of blocked designs
Post hoc classification of trials e.g. according to performance or subsequent memory
Some events can only be indicated by the subject e.g. spontaneous perceptual changes
Some trials cannot be blocked e.g. “oddball” designs

11. er-fMRI: “oddball” designs…
time

12. Advantages of er-fMRI
Randomised trial order c.f. confounds of blocked designs
Post hoc classification of trials e.g. according to performance or subsequent memory
Some events can only be indicated by subject e.g. spontaneous perceptual changes
Some trials cannot be blocked e.g. “oddball” designs
More accurate models even for blocked designs? “state-item” interactions

13. er-fMRI: “event-based” model of block-designs
“Epoch” model assumes constant neural processes throughout block U1 U2 U3 P1 P2 P3
“Event” model may capture state-item interactions
Data U1 U2 U3 P1 P2 P3
Model

14. Modeling block designs: epochs vs events
Designs can be blocked or intermixed,
BUT models for blocked designs can be
epoch- or event-related
Epochs are periods of sustained stimulation (e.g, box-car functions)
Events are impulses (delta-functions)
Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s)
In SPM, all conditions are specified in terms of their 1) onsets and 2) durations
… epochs: variable or constant duration
… events: zero duration
Sustained epoch
“Classic”
Boxcar
function
Series of events
Delta
functions
Convolved
with HRF

15. Disadvantages of er-fMRI
Less efficient for detecting effects than blocked designs.
Some psychological processes may be better blocked (e.g. task-switching, attentional instructions).

16. BOLD impulse response
Function of blood volume and deoxyhemoglobin content (Buxton et al. 1998)
Peak (max. oxygenation) 4-6s post-stimulus; return to baseline after 20-30s
initial undershoot sometimes observed (Malonek & Grinvald, 1996)
Similar across V1, A1, S1…
… but differences across other regions (Schacter et al. 1997) and individuals (Aguirre et al. 1998)
Brief
Stimulus
Undershoot
Initial
Peak

17. BOLD impulse response
Early er-fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baseline.
However, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodated…
… particularly if responses are assumed to superpose linearly.
Short SOAs can give a more efficient design (see below).
Brief
Stimulus
Undershoot
Initial
Peak

18. General Linear (Convolution) Model
For block designs, the exact shape of the convolution kernel (i.e. HRF) does not matter much.
For event-related designs this becomes much more important.
Usually, we use more than a single basis function to model the HRF.
GLM for a single voxel:
y(t) = u(t)  h(t) + (t)
u(t)
h(t)= ßi fi (t)
T 2T 3T ...
convolution
sampled each scan
Design Matrix

19. Temporal basis functions
Finite Impulse Response (FIR) model
Fourier basis set
Gamma functions set
Informed basis set

20. Informed basis set Canonical Temporal Dispersion
Canonical HRF (2 gamma functions)
plus Multivariate Taylor expansion in:
time (Temporal Derivative)
width (Dispersion Derivative)
F-tests allow testing for any responses of any shape.
T-tests on canonical HRF alone (at 1st level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is a reasonable fit.
Canonical
Temporal
Dispersion
Friston et al. 1998, NeuroImage

21. Temporal basis sets: Which one?
In this example (rapid motor response to faces, Henson et al, 2001)…
Canonical
+ Temporal
+ Dispersion
+ FIR
canonical + temporal + dispersion derivatives appear sufficient
may not be for more complex trials (e.g. stimulus-delay-response)
but then such trials better modelled with separate neural components (i.e. activity no longer delta function) (Zarahn, 1999)

22. left occipital cortex
right occipital cortex
Penny et al. 2007, Hum. Brain Mapp.

23. Timing Issues : Practical
TR=4s
Scans
Assume TR is 4s
Sampling at [0,4,8,12…] post- stimulus may miss peak signal
Stimulus (synchronous)
Sampling rate=4s
SOA = Stimulus onset asynchrony
(= time between onsets of two subsequent stimuli)

24. Timing Issues : Practical
TR=4s
Scans
Assume TR is 4s
Sampling at [0,4,8,12…] post- stimulus may miss peak signal
Higher effective sampling by:
1. Asynchrony, e.g. SOA = 1.5TR
Stimulus (asynchronous)
Sampling rate=2s
SOA = Stimulus onset asynchrony
(= time between onsets of two subsequent stimuli)

25. Timing Issues : Practical
TR=4s
Scans
Assume TR is 4s
Sampling at [0,4,8,12…] post- stimulus may miss peak signal
Higher effective sampling by:
1. Asynchrony, e.g. SOA = 1.5TR
2. Random jitter, e.g. SOA = (2 ± 0.5)TR
Better response characterisation (Miezin et al, 2000)
Stimulus (random jitter)
Sampling rate=2s
SOA = Stimulus onset asynchrony
(= time between onsets of two subsequent stimuli)

26. Slice-timing
T=16, TR=2s
Scan 1 o
T0=16 o
T0=9

27. Slice-timing
Top slice
Bottom slice
Slices acquired at different times, yet model is the same for all slices
=> different results (using canonical HRF) for different reference slices
Solutions:
1. Temporal interpolation of data … but less good for longer TRs
2. More general basis set (e.g. with temporal derivatives) … but more complicated design matrix
TR=3s
SPM{t}
SPM{t}
Interpolated
SPM{t}
Derivative
Henson et al. 1999
SPM{F}

28. NB: efficiency depends on design matrix and the chosen contrast !
Design efficiency
The aim is to minimize the standard error of a t-contrast (i.e. the denominator of a t-statistic).
This is equivalent to maximizing the efficiency ε:
Noise variance
Design variance
If we assume that the noise variance is independent of the specific design:
NB: efficiency depends on design matrix and the chosen contrast !
This is a relative measure: all we can say is that one design is more efficient than another (for a given contrast).

29.  = Fixed SOA = 16s Not particularly efficient… Stimulus (“Neural”)
HRF
Predicted Data  =
Not particularly efficient…

30.  = Fixed SOA = 4s Very inefficient… Stimulus (“Neural”) HRF
Predicted Data  =
Very inefficient…

31.  = Randomised, SOAmin= 4s More efficient … Stimulus (“Neural”) HRF
Predicted Data  =
More efficient …

32.  = Blocked, SOAmin= 4s Even more efficient… Stimulus (“Neural”) HRF
Predicted Data  =
Even more efficient…

33. Another perspective on efficiency
Hemodynamic transfer function (based on canonical HRF):
neural activity (Hz) → BOLD
Highpass-filtered
efficiency = bandpassed signal energy
Josephs & Henson 1999, Phil Trans B

34.  =  = Blocked, epoch = 20s Blocked-epoch (with short SOA)
Stimulus (“Neural”)
HRF
Predicted Data  =  =
Blocked-epoch (with short SOA)

35. Sinusoidal modulation, f = 1/33s
Stimulus (“Neural”)
HRF
Predicted Data  =  =
The most efficient design of all!

36. Blocked (80s), SOAmin=4s, highpass filter = 1/120s
Predicted data
(incl. HP filtering!)
Stimulus (“Neural”)
HRF =   =
Don’t use long (>60s) blocks!

37. Randomised, SOAmin=4s, highpass filter = 1/120s
Stimulus (“Neural”)
HRF
Predicted Data  =  =
Randomised design spreads power over frequencies.

38. Efficiency: Multiple event types
Design parametrised by:
SOAmin Minimum SOA
pi(h) Probability of event-type i given history h of last m events
With n event-types pi(h) is a nm  n Transition Matrix
Example: Randomised AB
A B A B
=> ABBBABAABABAAA...
4s smoothing; 1/60s highpass filtering
Differential Effect (A-B)
Common Effect (A+B)

39. Efficiency: Multiple event types
4s smoothing; 1/60s highpass filtering
Example: Null events
A B A B
=> AB-BAA--B---ABB...
Efficient for differential and main effects at short SOA
Equivalent to stochastic SOA (null event corresponds to a third unmodelled event-type)
Null Events (A-B)
Null Events (A+B)

40. Efficiency – main conclusions
Optimal design for one contrast may not be optimal for another.
Generally, blocked designs with short SOAs are the most efficient design.
With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for common effect (A+B) is 16-20s.
Inclusion of null events gives good efficiency for both common and differential effects at short SOAs.

41. But beware: Nonlinearities at short SOAs
stim. presented alone
stim. when preceded
by another stim. (1 s)
FIG. 1. Top panel: Simulated responses to a pair of words (bars) one second apart, presented together (solid line) and separately (broken lines) based on the kernels shown in Fig. 4. Lower panel: The
response to the second word when presented alone (broken line as above) and when preceded by the first (solid line). The latter obtains by subtracting the response to the first word from the response to both. The difference reflects the effect of the first word on the response to the second.
Friston et al. 2000, NeuroImage
Friston et al. 1998, Magn. Res. Med.

42. Thank you